Subcooled Flow Boiling Research Articles

3D Numerical Investigation of Bubble Upflow Condensation Behaviors During Subcooled Flow Boiling in Mini-Channel with VOSET

In the subcooled flow boiling process, bubble condensation is an inevitable basic phenomenon. This paper studies the condensation phenomenon of the single, double vertical/horizontal saturated bubbles rising in a three-dimensional mini-rectangular channel based on the interface capture method VOSET (coupled volume-of-fluid and level set method) and the phase transition model. Bubble condensation behaviors are investigated at different initial diameters, inlet velocity distributions, subcooling temperatures, bubble gaps, and arrangement for the two-bubble condensing system especially. The effects of these parametric on bubble motion trajectory, shape evolution, volume variation, and condensation rate are presented. The numerical results indicated that the initial bubble size and liquid subcooling play an important role in influencing the shape and volume variation of condensing bubble behaviors significantly, while the inlet velocity distribution only affects bubble motion trajectory. Furthermore, the interaction and coalescence between the bubbles will affect the bubble behaviors and the condensation rate. Finally, the condensation heat transfer coefficients at the bubble surfaces for different cases simulated in this paper are presented, seemingly first in the literature.

Numerical and experimental investigation of calcium sulfate crystallization fouling under upward subcooled flow boiling

In this paper, a quasi-unsteady mathematical model was presented to examine the crystallization fouling of the calcium sulfate aqueous solutions under upward subcooled flow boiling (SFB). An experimental set-up is also fabricated to collect experimental data for validating the model results. The developed model can axially and radially determine the temperature variation. An asymptotic predictive model was also used to calculate the heat transfer coefficients. Theoretical results of the bulk and surface temperatures at any desired location of the test section were coupled with the fouling formation equations to provide an integrated model for prediction of variable fouling resistance and deposit thickness along the heat transfer surface. Besides, variation of local heated surface and deposit surface temperatures as well as the pressure drop were theoretically evaluated over time while the deposit grows on the heated surface. The simulation results showed that reaction is the controlling mechanism when SFB is predominant.

Effect of Forced Convection Heat Transfer on Vapor Quality in Subcooled Flow Boiling

Abstract A new theoretical model based on energy balance and well-known heat transfer correlations is proposed for predicting vapor quality in subcooled flow boiling. This model takes into account the enhancement of forced convection heat transfer due to the presence of vapor. It is shown that the vapor quality predicted by our model is much less than that by a previous model for low pressure. This result demonstrates that the convective heat transfer coefficient cannot be constant, and the effect of gas phase on forced convection heat transfer cannot be neglected even for subcooled flow boiling, particularly at low pressures. However, the difference between the present and previous models decreases as the pressure increases, because (i) the increase of the convective heat transfer coefficient is weakened, and (ii) boiling heat transfer becomes dominant. Furthermore, the present model has the capability of locating the point at which bulk boiling commences.

Investigation of Wall Boiling Closure, Momentum Closure and Population Balance Models for Refrigerant Gas–Liquid Subcooled Boiling Flow in a Vertical Pipe Using a Two-Fluid Eulerian CFD Model

The precise design of heat exchangers in automobile air conditioning systems for more sustainable electric vehicles requires an enhanced assessment of CFD mechanistic models for the subcooled boiling flow of pure eco-friendly refrigerant. Computational Multiphase Flow Dynamics (CMFDs) relies on two-phase closure models to accurately depict the complex physical phenomena involved in flow boiling. This paper thoroughly examines two-phase CMFD flow boiling, incorporating sensitivity analyses of critical parameters such as boiling closures, momentum closures, and population balance models. Three datasets from the DEBORA experiment, involving vertical pipes with subcooled boiling flow of refrigerant at three different pressures and varying levels of inlet liquid subcooling, are used for comparison with CFD simulations. This study integrates nucleate site density and bubble departure diameter models to enhance wall boiling model accuracy. It aims to investigate various interfacial forces and examines the S-Gamma and Adaptive Multiple Size-Group (A-MuSiG) size distribution methods for their roles in bubble break up and coalescence. These proposed approaches demonstrate their efficacy, contributing to a deeper understanding of flow boiling phenomena and the development of more accurate models. This investigation offers valuable insights into selecting the most appropriate sub-closure models for both boiling closure and momentum closure in simulating boiling flows.

Numerical Study on Subcooled Boiling Flow and Heat Transfer Characteristics in Helical Cruciform Fuel Assembly

The helical cruciform fuel rod is a new fuel design. Its advantages include a large surface area–to-volume ratio, short thermal conductivity distance, and no need for grid spacers. This new fuel rod can effectively improve the hydraulic performance of nuclear reactors. To study the performance of the helical cruciform fuel assembly, the subcooled boiling flow and heat transfer characteristics of this assembly are analyzed in the present work based on computational fluid dynamics. The results indicate that the temperature distribution of the central rod wall surface in the circumferential direction has inhomogeneity and periodicity. The fluid’s temperature and velocity distribution in the cross section are high in the center and low elsewhere, and the fuel rod’s torsional orientation is compatible with the velocity vector’s direction. The vapor volume fraction on the wall of the center rod of the fuel assembly is the highest, and the vapor volume fraction in the mainstream area is relatively low. This work provides a reference for further research on helical cruciform fuel assemblies in the thermal analysis of nuclear reactors.

Thermal Characterization of Subcooled Flow Boiling in a Pin-Fin Coldplate With Non-Uniform Heating

Abstract Coldplates are a crucial component in various cooling applications, such as cooling data center servers and power electronics. The unprecedented growth in electronics power density, along with the resulting ultrahigh heat fluxes, demands a transition from single-phase forced convection to two-phase flow boiling heat transfer. The majority of studies in the literature have focused on flow boiling in fin-enhanced silicon microgaps and microchannels, with only a few addressing flow boiling in millimeter-scale heat sinks. In the present study, flow boiling of HFE-7200 dielectric fluid in a millimeter-scale pin-fin coldplate is experimentally investigated under nonuniform heating conditions. Four background heaters represent the low-dissipating-power devices. On the other hand, five hotspot heaters mimic the high-heat-flux devices and generate heat fluxes ranging from 50 W/cm2 to 1000 W/cm2, corresponding to hotspot heat inputs ranging from 62.5 W to 1.25 kW, respectively. The coldplate's thermohydraulic performance is investigated for various flow rates and inlet temperature ranging from 0.5 L/min to 1.5 L/min and from 25 °C to 60 °C, respectively. A high-speed camera is utilized for a narrow field of view (FOV) flow visualization at a frame rate of 2229 fps while a digital camera is used for a wider FOV at 60 fps. Flow visualization demonstrated the transition between bubbly, slug/churn, and stratified two-phase flow regimes.

Computational Analysis of Subcooled Flow Boiling in a Vertical Minichannel with Two Different Shapes under Various Mass Fluxes

In the current research project, two-dimensional numerical simulations are conducted to analyze the effects of geometrical configuration on flow structures and the thermal performances of subcooled flow boiling. The CFD simulations are carried out in two different configurations (straight and periodic constriction expansion) in a minichannel mounted vertically at four mass fluxes (500 kg/m2s; 836.64 kg/m2s; 1170 kg/m2s; and 2535 kg/m2s). The present predicted results exhibit excellent accordance with the previous experiments, with mean errors of 6.39% and 9.78%, demonstrating the efficiency of the present numerical study. The simulation results show that the periodic constriction expansion design provides good mixing between the layers, leading to a 43.11% mean enhancement of the thermal transfer, which is more important than the slight pressure drop penalty of 4.32 for a mass flux of 500 kg/m2s due to the combined pressure drop along the minichannel that resulted from the periodic constriction and expansion regions. Furthermore, the visualization of flow patterns shows that the bubbly flow is the dominant flow regime in the periodic constriction-expansion configuration.

The Numerical Investigations of Heat Transfer and Bubble Behaviors of R22 in Subcooled Flow Boiling in Casing Tubes

Amidst the background of “double carbon”, energy saving and emission reduction is a popular direction in the current refrigeration industry. Therefore, the research on the boiling heat transfer of gas–liquid two-phase flow is helpful to strengthen the heat transfer and design a more efficient heat exchanger. In this paper, a research method combining numerical simulation and experimental verification is adopted. Firstly, an experimental platform used for the subcooled flow boiling of refrigerant in casing tubes is introduced and experiments are carried out to obtain experimental data, which provides a theoretical basis for the development of numerical simulation and verifies the feasibility of numerical simulation. A numerical model of subcooled flow boiling in R22 was established and the grid independence test was carried out. Based on the simulation results, three factors affecting the boiling heat transfer of R22 are analyzed: First, the boiling heat transfer coefficient of R22 increases with the increase of the mass flow rate of R22, but the increase decreases when the mass flow rate increases from 0.018 kg/s to 0.020 kg/s. Second, the boiling heat transfer coefficient of R22 increases significantly with the increase of hot water flow rate. Third, the influence of R22 subcooling on boiling heat transfer is more complex. When the subcooling is 5 °C and 1 °C, heat transfer can be enhanced; high subcooling at 5 °C can enhance convective heat transfer and low subcooling at 1 °C can accelerate the arrival of saturated boiling. In this paper, three kinds of bubble behaviors affecting heat transfer in supercooled flow boiling, including sliding, polymerization, and bounce are also studied, which provides a basis for further research on heat transfer mechanism of supercooled flow boiling.

Numerical Simulation of Subcooled Flow Boiling in a Threaded Tube and Investigation of Heat Transfer and Bubble Behavior

Three-dimensional subcooled flow boiling of R134a in a threaded tube was numerically simulated at the conditions of 200~400 kW/m2 heat flux, 3~20 K inlet subcooling, and 0.2~0.6 m/s inlet velocity. The bubble behavior in the horizontal threaded tube with 0.581 mm thread tooth height was observed. The effect of heat flux, inlet subcooling, and inlet velocity on bubble departure diameter and heat transfer coefficient were explored. The results presented the whole growth process of five kinds of bubbles. It was found that the bubbles either collapsed in cold liquid after leaving the heating wall or grew along the axial direction and contacted the heating wall. And there was no bubble sliding during the growth. In addition, the most important and special characteristic of bubble behavior in threaded tubes was the phenomenon of the bubble passing through the cavity. The coalescence and breakup behavior occurred after the bubble passed through the cavity. According to the discussions of the departure diameter and heat transfer coefficient, it was inferred that the bubble departure diameter increased with the increase of heat flux from 200~400 kW/m2 and subcooling from 3~20 K while decreasing with the increase of inlet velocity from 0.2~0.6 m/s. And due to the influence of the threaded tube structure, there are special points in the change of bubble departure diameter. The heat transfer coefficient of the bubbles in the threaded tube was higher than the smooth tube, which was increased by 1.5~12.5%. The heat transfer coefficient increased with the increase of heat flux and subcooling and is closely related to the bubble departure diameter.

Unsteady heat transfer characteristics of R-407C in the subcooled flow boiling stemming from the oscillating refrigerant flow rate

The objective of this experiment is to investigate the unsteady heat transfer of R-407C subcooled flow boiling (SCFB) due to the oscillating refrigerant flow rate within a narrow tube oriented horizontally for application in energy efficiency air conditioning system. The refrigerant flow rate is input in the cycle of triangular oscillations. Influences of oscillation amplitude (ΔG/G‾) and oscillation period (tp) of the periodic flow rate on SCFB heat transfer are studied. The present results disclose that either ΔG/G‾ or tp has minor impact on time-average SCFB heat transfer performance. However, obvious changes in the temporal variations of the wall temperature on the pipe (Tw) and convective heat transfer coefficient (hr) are found, leading to three heat transfer mechanisms of single phase convection, intermittent nucleate boiling, and persistent subcooled boiling for various input heat fluxes. The Tw of persistent subcooled boiling presents the reversed tendency compared to that of single phase convection due to the variation of the triangular R-407C oscillation. In the case of intermediate heat flux, the unusual boiling phenomenon, called intermittent nucleate boiling, can be obtained depending on the R-407C mass flux. The visualized bubble images are also provided to further describe the intermittent nucleate boiling.

Bubble Sliding Characteristics and Dynamics of R134a during Subcooled Boiling Flow in a Narrow Gap

The numerical method was used to study bubble sliding characteristics and dynamics of R134a during subcooled flow boiling in a narrow gap. In the numerical method, the volume of fraction (VOF) model, level set method, Lee phase change model and the SST k − ω turbulent model were adopted for the construction of the subcooled flow boiling model. In order to explore bubble sliding dynamics during subcooled flow boiling, the bubble sliding model was introduced. The bubble velocity, bubble departure diameter, sliding distance and bubble sliding dynamics were investigated at 0.2 to 5 m/s inlet velocities. The simulation results showed that the bubble velocity at the flow direction was the most important contribution to bubble velocity. Additionally, the bubble velocity of 12 bubbles mostly oscillated with time during the sliding process at 0.2 to 0.6 m/s inlet velocities, while the bubble velocity increased during the sliding process due to the bubble having had a certain inertia at 2 to 5 m/s inlet velocities. It was also found that the average bubble velocity in flow direction accounted for about 80% of the mainstream velocities at 0.2 to 5 m/s. In the investigation of bubble sliding distance and departure diameter, it was concluded that the ratio of the maximum sliding distance to the minimum sliding distance was close to two at inlet velocities of 0.3 to 5 m/s. Moreover, with increasing inlet velocity, the average sliding distance increased significantly. The average bubble departure diameter obviously increased from 0.2 to 0.5 m/s inlet velocity and greatly reduced after 0.6 m/s. Finally, the investigations of the bubble sliding dynamics showed that the surface tension dominated the bubble sliding process at 0.2 to 0.6 m/s inlet velocities. However, the drag force dominated the bubble sliding process at 2 to 5 m/s inlet velocities.

Performance Comparison of ANN-Based Model and Empirical Correlations for Void Fraction Prediction of Subcooled Boiling Flow in Vertical Upward Channel

The accurate prediction of void fraction parameter in subcooled boiling flow is very important for nuclear safety since it has significant influences on the mass flow rate, the onset of two-phase flow instability, and the heat transfer characteristics in a nuclear reactor core. Many different models and empirical correlations have been established over a variety of input conditions; however, this classical approach could lead to unsatisfactory prediction due to the uncertainties of model parameter and model forms. To cope with these limitations, Artificial Neural Network (ANN) is a powerful machine learning tool for modeling and solving non-linear and complicated physical problems. Therefore, this work is aim at developing an ANN-based model to predict the local void fraction of subcooled boiling flows. The comparison results of the performance between the ANN-based model and empirical correlations for the void fraction prediction of subcooled boiling in vertical upward channel showed the potential use of ANN-based model in the Computational Fluid Dynamics (CFD) codes to accurately simulate the subcooled boiling phenomena.

Heat Transfer Deterioration by the Copper Oxide Layer on Horizontal Subcooled Flow Boiling

Water–copper is one of the most common combinations of working fluid and heating surface in high-performance cooling systems. Copper is usually selected for its high thermal conductivity and water for its high heat transfer coefficient, especially in the two-phase regime. However, copper tends to suffer oxidation in the presence of water and thus the heat flux performance is affected. In this research, an experimental investigation was conducted using a cooper bare surface as a heating surface under a constant mass flux of 600 kg·m−2·s−1 of deionized water at a subcooled inlet temperature ΔTsub of 70 K under atmospheric pressure conditions on a closed-loop. To confirm the heat transfer deterioration, the experiment was repeated thirteen times. On the flow boiling region after thirteen experiments, the results show an increase in the wall superheat ΔTsat of approximately 26% and a reduction in the heat flux of approximately 200 kW·m−2. On the other hand, the effect of oxidation on the single phase is almost marginal.

STUDY ON HEAT TRANSFER CHARACTERISTICS AND STABILITY OF SUBCOOLED FLOW BOILING IN A NOVEL BOTTOM-DIVERGING MICROCHANNEL WITH EQUAL CROSS-SECTIONAL AREA

The enhancement of boiling heat transfer and its stability have been widely studied in the field of flow boiling in microchannel heat sinks. In this study, a novel diverging microchannel is proposed to enhance the heat transfer performance and boiling stability during subcooled flow boiling in the microchannel by the channel structure of divergent fluid-solid coupling bottom interface and equal cross-sectional area. Two-phase patterns, heat transfer characteristics, and pressure variations of subcooled flow boiling of HFE-7100 in this microchannel, its reversal flow microchannel, uniform microchannel, and diverging microchannel are compared under different heat flux conditions. The results show that the microchannel structure directly affects the nucleation time of bubbles and their behavior. At the same heat flux, the bubble nucleation time in the bottom-diverging microchannel with equal cross-sectional area is the longest, the bubble size is the smallest and the closest to the exit of the microchannel, which is beneficial to rapidly exhaust of the bubbles. The bottom-diverging microchannel with equal cross-sectional area exhibits higher heat transfer coefficient and smaller pressure fluctuation than its reversal flow microchannel, uniform microchannel, and diverging microchannel.

Numerical Simulation of Subcooled Flow Boiling in a Vertical Annulus Channel Under Near Atmospheric Pressure Conditions

In the present study, a Eulerian-Eulerian two-fluid model is developed to analyze the flow boiling phenomena under near-atmospheric pressure conditions. The required constitutive correlations for the two-fluid model are provided as flow regime dependent within the algebraic interfacial area density framework. The two-fluid model developed with Rensselaer Polytechnic Institute (RPI) wall heat flux partitioning is used to analyze the subcooled nucleate boiling of water at low pressure in three vertical annulus channels of different heated lengths over a wide range of inlet mass flux, wall heat flux, and inlet subcooling conditions. The subcooled water enters the heated annulus channel from the bottom end and is heated to near-saturation temperature. Upon reaching the saturation temperature, the wall boiling generates dispersed vapor bubbles near the heated wall. Farther along the heated length, larger bubbles can be formed by coalescence and evaporation, and the bubbles move on to the channel core region with increased vapor fraction so the flow regime changes from bubbly to transition regime. Farther along, it may turn to an annular flow regime. The benchmark experimental cases chosen are used to validate the model capability in predicting the bubbly flow and transition flow regime (slug flow regime) characteristics with the proposed methodology. Further, the low-pressure boiling model developed is successfully extended to predict the liquid sodium boiling in flow channels similar to sodium-cooled fast reactor fuel subchannels using suitable interfacial correlations.

Numerical Simulation Research of Bubble Characteristics and Bubble Departure Diameter in Subcooled Flow Boiling

Three-dimensional subcooled flow boiling of R134a in a horizontal tube was simulated by a VOF (volume of fluid) model combined with the level set method. Bubble characteristics were explored at heat flux of 0.3 MW/m2, inlet subcooling of 3 K, and inlet velocity of 0.4 m/s. It was observed that five representative bubbles occurred in subcooled flow boiling, including sliding bubble, coalescing bubble, non-departed bubble, bouncing bubble, and continuous-boiling bubble. The results showed that the bubble radial velocity was an important factor of bubble departure after a sliding process. Moreover, the effect of heat flux, inlet velocity, and inlet subcooling on bubble departure diameter were investigated. The departure diameter increased with increasing inlet velocity from 0.2 to 0.4 m/s and heat flux from 0.2 to 0.4 MW/m2, while diameter decreased with inlet subcooling from 3 to 10 K. Finally, based on the influence of heat flux, inlet velocity, and inlet subcooling on average departure diameter of the bubble except the coalescing bubble, a model was proposed to predict the average departure diameter. The deviation of the model was within 5%.

Prediction of Critical Heat Flux for Subcooled Flow Boiling in Annulus and Transient Surface Temperature Change at CHF

The ability to predict critical heat flux (CHF) is of considerable interest for high-heat equipment, including nuclear reactors. CHF prediction from a mechanistic model for subcooled flow boiling in rod bundles still remains unsolved. In this paper, we try to predict the CHF in an annulus, which is the most basic flow geometry simplified from a fuel bundle, using a liquid sublayer dryout model. The prediction is validated with both water and R113 data, showing an accuracy within ±30%. After the CHF in an annulus is calculated successfully, a near-wall vapor–liquid structure is proposed on the basis of the liquid sublayer dryout model. Modeling of heat transfer modes over the heating surface at CHF is performed, and predictions of the changes in liquid sublayer thickness and heater surface temperature at the CHF occurrence point are carried out by solving the heat conduction equation in cylindrical coordinates with a convective boundary condition, which changes with the change in flow pattern over the heating surface. Transient changes in the liquid sublayer thickness and surface temperature at the CHF occurrence point are reported.

Numerical Study of the Effect of the Rolling Motion on the Subcooled Flow Boiling in the Subchannel

The marine environment may change the force on the fluid and inevitably influence bubble behavior and the two-phase flow in the reactor core, which are vital to the safety margin of a nuclear reactor. To explore the effect of the marine motion on the flow and heat transfer features of subcooled flow boiling in the reactor core, the volume of fluid (VOF) method is employed to reveal the interaction between the interface structure and two-phase flow in the subchannel under rolling motion. The variations of several physical parameters are obtained, including the transverse flow, the vapor volume fraction, the vapor adhesion ratio, and the phase distribution of boiling two-phase flow with time. Sensitivity analyses of the amplitude and the period of the rolling motion were performed to demonstrate the mechanisms of the influence of the rolling motion. We found that the transverse flow in the subchannel was mainly affected by the Euler force under the rolling motion. In contrast to the two-phase flow in the static state, the vapor volume fraction and vapor adhesion ratio show different characteristics under rolling motion. Additionally, the onset of significant void (OSV) point changes periodically under rolling motion.

Numerical Simulation Study on the Flow and Heat Transfer Characteristics of Subcooled N-Heptane Flow Boiling in a Vertical Pipe under External Radiation

In the top submerged lance (TSL) smelting process, flow boiling may occur in the lance’s inner pipe due to the heat coming from the furnace when liquid fuel is adopted. In the current study, a numerical simulation was carried out by coupling the Eulerian two-fluid model with the improved RPI wall boiling model to investigate the subcooled n-heptane flow boiling in the inner pipe. The effects of inlet velocity and pipe wall emissivity on two-phase flow and heat transfer are elucidated. The results show that, for pipes with inlet velocity ranging from 0.3 m·s−1 to 1.0 m·s−1, an increase in inlet velocity leads to a lower void fraction near the outlet, as well as a lower average velocity and a lower average temperature of each phase. Meanwhile, the Onset of Nucleate Boiling (ONB) position approaches to the outlet, and the total pressure drop of the entire pipe reduces when the inlet velocity increases. However, the opposite trends appear when increasing the pipe wall emissivity. The maximum wall temperature corresponding to the critical heat flux (CHF) point is slightly affected by inlet velocity but significantly affected by pipe wall emissivity. The non-equilibrium effect and the specific components of pressure drop are also further investigated.

Comparison of Intergroup Mass Transfer Coefficient Correlations in Two-Group IATE for Subcooled Boiling Flow

The interfacial area concentration (IAC) is of vital importance in determining the interfacial transfer terms of mass, momentum, and energy between phases in the two-fluid model. The two-group (2-G) interfacial area transport equation (IATE) dynamically models the IAC evolution of large and small bubbles, and the intergroup transfer bookkeeps the mass transferring between two groups. Different intergroup mass transfer coefficient correlations are employed in the 2-G IATE model, which include one old correlation and three new correlations previously developed by the authors. The two-group IATE is benchmarked with subcooled boiling experimental dataset. The group-1 interfacial area concentration results show that the three modified correlations improve the physically incorrect prediction by the old correlation. With the modified correlations, the 2-G IATE is foundationally capable of predicting the group-1 interfacial area concentration in subcooled boiling flow.